Disk space shortage wreaks havoc on a domain controller

One day our Windows 2003 domain controller ran out of disk space, and a slew of problems ensued. Apparently, Active Directory synchronization failed due to insifficient space, and the event log was full of messages like this:

Event Type: Warning
Event Source: NETLOGON
Event Category: None
Event ID: 5705
Description:
The change log cache maintained by the Netlogon service for  database changes is inconsistent. The Netlogon service is resetting the change log.

Event Type: Warning
Event Source: W32Time
Event ID: 26
Description:
Time Provider NtpClient: The response received from domain controller  has a bad signature. The response may have been tampered with and will be ignored.

Event Type: Error
Event Source: NETLOGON
Event ID: 5805
Description:
The session setup from the computer  failed to authenticate. The following error occurred: 
Access is denied. 

Event Type: Warning
Event Source: LSASRV
Event Category: SPNEGO (Negotiator) 
Event ID: 40960
Description:
The Security System detected an authentication error for the server cifs/.  The failure code from authentication protocol Kerberos was "The attempted logon is invalid. This is either due to a bad username or authentication information. (0xc000006d)".

Event Type: Error
Event Source: Kerberos
Event ID: 4
Description:
The kerberos client received a KRB_AP_ERR_MODIFIED error from the server host/.  The target name used was ldap//@. This indicates that the password used to encrypt the kerberos service ticket is different than that on the target server. Commonly, this is due to identically named  machine accounts in the target realm (), and the client realm.   Please contact your system administrator.

Event Type: Error
Event Source: NETLOGON
Event ID: 3210
Description:
This computer could not authenticate with \\, a Windows domain controller for domain , and therefore this computer might deny logon requests. This inability to authenticate might be caused by another computer on the same network using the same name or the password for this computer account is not recognized. If this message appears again, contact your system administrator.

Even after freeing some space, problems continued, since Active Directory database was damaged. The solution was to reset computer domain password using netdom, as documented in Microsoft KB article 260575